Why does the square root of negative 9 give an answer instead of an error?
In lower school mathematics we are taught that the square root of a negative number does not exist. In fact, it does exist – it just isn’t a ‘real’ number. There is a whole branch of mathematics concerned with what are called ‘imaginary’ or ‘complex’ numbers and the calculator is designed to allow their use because they are part of some of the upper school courses. You can recognise a complex number by the way the calculator writes it – as (0,3) or (2.13,-1.7). Any time that you see an answer written in brackets it means that the number is complex. This affects the POLYROOT function too. If you use POLYROOT to solve the quadratic equation of x^2+4x+5=0, which does not cross the x axis (try graphing it!) you will find that it gives the roots as complex numbers. They are NOT (x,y) points on the x, y axes! Don’t use them – just write “No real solution”. ie.POLYROOT([1,4,5]) gives [(-2,1),(-2,-1)] Another similar problem is with the inverse trig functions. Since sine and cosine have ranges
